Dear Damien: The map is given as finite, so what is ZMT telling us that we don't see by more elementary means (say working over open affines in $Y$, as we may do to verify what you claim)?

Since it is finite flat of degree 2, Zariski-locally on the base it is ${\rm{Spec}}(A)\rightarrow{\rm{Spec}}(B)$ where 1 is part of a $B$-basis $\{1,a\}$ of $A$. If $T^2-uT+v$ is the characteristic polynomial of $a$-multiplication on $A$ then $B[T]/(T^2-uT+v)\rightarrow A$ via $X\mapsto a$ is an isomorphism. Then $T \mapsto u-T$ is an $A$-automorphism that does the job when $T^2-uT+v$ is separable over Frac($B$).

Another thought, inspired by the case over fields: if the underlying quadratic space is split (as can be arranged over an etale cover) then perhaps the octonion algebra is already split. The proofs I've seen of this fact over fields are too specific to the field case to carry over to artin local rings, but maybe there's a way to do it, and thereby avoid any cohomological pain.

Dear Daniel: Before I posed the question I was well aware that constructing a suitable cohomology theory is a natural approach and would do the job -- that is the entire reason that I wrote Remark 2. I don't think we're getting anywhere with this discussion (as it isn't telling me anything I didn't know before I posted the question). Regards,

@Daniel: How is the deformation theory of Lie algebras (which I am well aware of) helpful in understanding deformations of octonions? I don't see any connection. I did wonder when writing "non-associativity" if someone might note that deformation theory for Lie algebras work nicely, but I didn't worry about it since I couldn't see how it helps. If it does, please enlighten me.

@Mariano: Sure, I agree, but as I said, I have no idea how to put in such links, so I tried what seemed like the next best thing. Anyway, I have followed v08itu's suggestion and put in the .pdf link to the paper, but it seems the link isn't "active"; again, I have no idea how to do such things, so please feel free to improve it if you know how.

@Mariano: (i) because I don't know how, and (ii) to compensate for (i) it seems entirely sufficient that I gave the title in full so that anyone who wishes can find it (or just type "octonion algebra", "deformation theory" into Google, which is how I found it). If you'd like to edit in the link, please feel free to do so.